DETERMINATION OF THE APPARENT THERMAL DIFFUSIVITY OF A NONUNIFORM SOIL1

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Abstract
In this report, we compare three methods (second- and third-order Taylor polynomials and cubic spline) for determining the apparent soil thermal diffusivity as a function of depth through the analysis of time-depth observations of soil temperature. Three methods are tested by using both field data measured in the upper 0.10 cm of soil in a corn field and hypothetical data generated by numerical approximation of the partial differential heat transfer equation. The field and generated data are fitted with Fourier series for estimating the temperature parameters (amplitude and phase angle of the temperature wave) and the heat flux phase. The second- and third-order Taylor polynomials and cubic splines are used to estimate the change of temperature parameters with depth. Theories describing heat transfer in uniform and non-uniform soil both use the temperature parameters to calculate soil thermal diffusivity. In general, the cubic spline approach provides reliable values of the apparent soil thermal diffusivity, whereas the second- and third-order Taylor polynomials for the case of nonuniform soil heat transfer sometimes provide physically unrealistic negative values. The results also show the failure of the uniform soil heat transfer theory (amplitude and phase equation) for estimating the thermal diffusivity in non-uniform soil.

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